The present invention relates generally to a novel optical system, and particularly to an optical system which provides light of increased intensity in the peripheral area of an object to be illuminated so that it is particularly useful for an illumination system or a projection system applicable to exposure of printed circuit boards, integrated circuits or the like, for exposure systems applicable to contact exposure apparatus for plate making, step-and-repeat machines or the like, and for illumination systems applicable to copy machines or the like.
It is well known that a conventional relay condenser optical system such as shown in FIG. 1 has been used in an illumination system which is intended to provide uniform illumination light for an entire object area effectively. The conventional condenser optical system, referring to FIG. 1, comprises a condenser lens C and a field lens F. The condenser optical system is designed so that the real image of a light source LS, which is s placed in front of the condenser lens C, is formed adjacent to the field lens F, and the real image of an entrance pupil A of the condenser lens C is formed on an object S which is placed behind the field lens F.
The conventional condenser optical system, however, raises a serious problem, i.e. the irradiance in the peripheral area of the object is reduced, as shown in FIG. 2, in accordance with the cosine fourth law. For instance, referring to FIG. 1, the irradiance at the point of the object where the exit angle .theta. is 27 degrees relative to the optical axis is less than that at the point on the optical axis, i.e. the point where the exit angle .theta. is zero degrees.
There are several reasons, other than the above-mentioned cosine fourth law, for the occurrence of irradiance reduction in the peripheral area of the object, which will be discussed in detail later. Actually, the irradiance in the peripheral area of the object is reduced less than a value derived from the cosine fourth law. According to the simulation calculation made by applying lens data listed in Table 1 to the optical system shown in FIG. 1, it is found that the irradiance at the point where the exit angle .theta. is 27 degrees, is reduced by 50 percent in comparison with the irradiance at the center thereof.
TABLE 1 ______________________________________ r d n ______________________________________ 1 0.77 0.37 1.5 2 .infin. 0.46 3 0.77 0.37 1.5 4 .infin. ______________________________________ f = 1, distance from the light source = 50, distance from the object = 100
FIG. 3 shows an irradiance distribution on the object P, which is obtained by using the optical system shown in FIG. 1, in the case where a point source is positioned on the optical axis at the distance of 50 units away from the optical system. FIG. 4 shows an irradiance distribution of the meridional ray on the object P, and FIG. 5 shows an irradiance distribution of the sagittal ray on the object P, in each of which the point source is positioned away by 14 units from the optical axis and at a distance of 50 units from the optical system. The respective vertical axis of FIGS. 3 through 5 depicts a relative irradiance, in which the irradiance of the center of the object P is regarded as 100 percent when the point source is positioned on the optical axis. On the other hand, the respective horizontal axis of FIGS. 3 through 5 depicts a position on the object P. In FIGS. 3 through 5, the position denoted by 50 units corresponds to the position on which the exit light from the optical system is impinged.
As mentioned above, the irradiance in the peripheral area of the object P is actually reduced less than a value derived from cosine fourth law. One of the reasons therefor is an aberration, because the cosine fourth law is on the premise that an optical system has no aberration, whereas an actual optical system inevitably has some aberration.
It has then conventionally been practiced that an optical system is designed so that the aberration should be eliminated as far as possible, in other words it has commonly been practiced that an optical system is designed so as to satisfy the sine condition. Thus, even in an illumination system, the optical system for use in illumination has conventionally been designed so as to satisfy the sine condition, because it has been believed to be matter of course by a person skilled in the art.
It has been found by the inventors, however, that designing an optical system so as to satisfy the sine condition causes an irradiance reduction in the peripheral area of the object to be illuminated.
Now the reasons why there is irradiance reduction in the peripheral area of the object will be discussed.
Referring to FIG. 6, which is a schematic view of an optical system, light emitted from the light source LS enters into the optical system at the entrance height h, in this case the light source LS can be regarded as being placed at an infinite distance from the optical system, because it is positioned at a far distance from the optical system in comparison with the focal length thereof. The real image of the light source LS is formed at a point I, and the light goes through an exit pupil at an exit angle .theta.. Satisfying the sine condition means that the sine of the exit angle .theta. is proportioned to the entrance height h; accordingly the relation can be expressed by the following formula (1): EQU h=k.sub.1 .multidot.sin .theta. (1)
where k.sub.1 is a proportional constant.
The light which entered into the optical system at the entrance height h exits therefrom to impinge upon the point Q of the object P. Then, sin .theta. can be expressed by the following formula (2): ##EQU1## where H is the distance between the point Q and the center of the object P (hereinafter referred to as illumination height), and a is the distance between the point I and the point Q.
It can then be transformed from the formulae (1) and (2), as follows: ##EQU2##
As can be understood from FIG. 6, when the incident height h is increased, the exit angle .theta. will become large, hence the illumination height H will be increased in accordance therewith, and similarly the distance a between the point I and the point Q will also be increased. In the case where the entrance height h is increased at a constant rate, the illumination height H will be rapidly increased more than the increase of the entrance height h, since the illumination height H is proportioned to the product of the distance a and the incident height h, as can be seen from the formula (3). The relationship between the incident light radius A.sub.0 around the optical axis in the entrance pupil A and the radius P.sub.0 of the illumination area of the object P, similarly to the relationship between the incident height h and the illumination height H, is that the radius P.sub.0 increases at a greater rate than the rate at which the radius A increases, from which it will be apparent that the irradiance on the object P will be reduced as it goes away from the optical axis, in comparison with that on the entrance pupil A.
Indeed in an image-formation optical system design it will be necessary to design the optical system so as to satisfy the sine condition because it is important to minimize the aberration, but in an illumination optical system design there is no need to do so. Furthermore, designing to satisfy the sine condition causes the irradiance reduction in the peripheral area of the object to be illuminated, as mentioned above.
In a conventional illumination system, it has been practiced, in order to correct the irradiance reduction in the peripheral area of the object, that a gradient filter is placed in the optical path thereof, or that the light source is placed at a sufficient distance from the object. These conventional correction methods are, however, disadvantageous in view of the fact that light quantity is considerably reduced in the entire area of the object in the former method, and that the illumination system inevitably becomes large in size in the latter.
Furthermore, it may often be required that irradiance in the peripheral area of an object is increased in comparison with that at the center thereof. For instance, in the case where an illumination apparatus when employing a projection lens is placed optically behind an original to be reproduced, an image projected on a photosensitive material will be affected by the cosine fourth law even if uniform irradiance is given throughout the original.